Consider a durable goods setting where consumers have discrete values and a monopolist is selling over 2 periods t = f1, 2g. There are two consumers- one who has a high per period value VH and one who has a low per period value VL. We assume that high value consumers have a much higher value than the low value consumers or VH > 2VL. For simplicity, cost of production is assumed to be 0. It is assumed that both the seller and the buyers discount at rate d. Thus, a consumer of type i 2 fH, Lg has value Vi for using the good for one period and value Vi(1 + d) when she buys the good in period 1 and uses it for both periods.
(a) Suppose the monopolist can lease the good in each period. What rental prices would he charge in each period? What is his profit (keep in mind his discounting).
(b) Now calculate, the optimal pricing policy when the monopolist can commit to prices p1, p2 at the beginning of the game. Remember that when the monopolist can commit, he cannot change the price p2, once period 2 arrives depending on what happened in period 1. Keep in mind that consumers are forward looking and the monopolist knows this.
(c) Compare the profit from selling in part (b) to the profit from leasing in part (a) and provide intuition. Now lets try and derive an equilibrium when the monopolist cannot pre-commit to prices.
(d) Suppose buyers of type i 2 fH, Lg play the following strategy: Buy in the first period if p1 Vi(1+ d); if not, wait for period 2 and buy if p2 Vi. What is the best response of the monopolist to this strategy?
(e) Now argue that the strategies from part (d) constitute an equilibrium.
(f) Compare the profit of the monopolist from parts (e), (a) and (b). In which case is the monopolist better off? How does this differ from the result we found in the lecture?